New Algorithms for Blind Equalization: The Constant Norm Algorithm Family

Abstract

In this paper, a new, efficient class of blind equalization algorithms is proposed for use in high-order, two-dimensional digital communication systems. We have called this family: the Constant Norm Algorithms (CNA). This family is derived in the context of Bussgang techniques. Therefore, the resulting algorithms are very simple. We show that some well-known blind algorithms such as "Sato's algorithm" or the Constant Modulus Algorithm (CMA) are particular cases in our CNA family. In addition, from this class, a new cost function, named Constant sQuare Algorithm (CQA), is derived, which is well designed for QAM. It results in a lower algorithm noise without increasing the complexity. Another advantage of this class lies in the possibility of creating new norms by combining several existing norms in order to benefit from the advantages of each original norm. For example, we present the norm resulting from the combination of the two algorithms, CMA and CQA. Moreover, we highlight that, with regard to the excess mean-square error performance, there is an optimal norm for each constellation, i.e., each modulation, in order to equalize it blindly